Re: Lizard engines and rat engines


"Tim Tyler" <tim@xxxxxxxxxxx> wrote in message news:dbbmln$2h2m$1@xxxxxxxxxxxxxxxxxxxxxx
> Perplexed in Peoria <jimmenegay@xxxxxxxxxxxxx> wrote or quoted:
> > "Inman Harvey" <inmanh@xxxxxxxxxxxxxxx> wrote in message news:db8mn9$1cgt$1@xxxxxxxxxxxxxxxxxxxxxx
>
> > > ... The Maximum Entropy Production principle [MEP]
> > > [NB: perfectly in accordance with Prigogine's 'law of minimum
> > > entropy production' -- the scenarios and boundary conditions are
> > > different] ...
> >
> > Yes, I can see how that might be the case. The physically expected
> > result is the max over one set of variational parameters, but the
> > min over another set of variational parameters.
> >
> > It is amusing to recall that we got to this point in the discussion
> > because Guy Hoelzer - thinking only of the MEP and not of Prigogine's
> > theorem - wanted to to interpret this maximization as teleological
> > (or at least to speak of it metaphorically as teleological).
> >
> > But this plan fails if we are simultaneously maximizing (over one
> > set of parameters) and minimizing (over a different set). Is the
> > teleological goal to maximize or minimize?
> >
> > Hmmm. Do we know of any goal-driven scheme in which the solution
> > is a minimum over one set and a maximum over a different set.
> > A "minimax"? Didn't von Neuman come up with something like that?
> > Two goal-directed Actors, each independently choosing from His/Her
> > own set of control variables, but Their goals are diametrically
> > opposed?
>
> Optimisation problems can have criteri that pull in multiple
> conflicting directions at once.

But in simple, "one player" optimizations, the conflict is resolved
by choosing a single, simple "objective function" which makes the
necessary compromises. You then do a single-minded optimization of
that compromise objective. Game theory is different and zero-sum
game theory is completely different. Now you have two attempts
to optimize going on simultaneously. If the objectives are diametrically
opposed, as they are in a non-zero game (maximize entropy production
over some domain of variation, but minimize it over some other domain)
then you get a "solution" which is a minimax.

> However in this case, the issue is probably not too significant:
> the maximum entropy guys are mostly saying that their schemes
> are significant far from equilibrium - where there's a chance of
> self-organising systems forming on the available energy gradients.
>
> By contrast, Prigogine's idea applies under just the opposite set of
> circumstances - when the system is near to equilibrium - so perhaps
> there's not much chance of a conflict of maximands.

True, but if you are doing a finite element analysis, you are going
to be close to equilibrium locally at all elements, and only far
from equilibrium globally.

Prigogine's theorem and MEP really do need to cohabit - you can't
claim that they never come into contact.

Incidentally, I am not insisting on my game-theory interpretation
of the situation - I am merely pointing out the amusing implications
if you insist on bringing teleology into thermodynamics.


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